On third homologies of groups and of quandles via the Dijkgraaf–Witten invariant and Inoue–Kabaya map

Takefumi Nosaka

研究成果: Contribution to journalArticle査読

5 被引用数 (Scopus)

抄録

We propose a simple method for producing quandle cocycles from group cocycles by a modification of the Inoue–Kabaya chain map. Further, we show that, with respect to “universal extension of quandles”, the chain map induces an isomorphism between third homologies (modulo some torsion). For example, all Mochizuki’s quandle 3–cocycles are shown to be derived from group cocycles. As an application, we calculate some Z–equivariant parts of the Dijkgraaf–Witten invariants of some cyclic branched covering spaces, via some cocycle invariant of links.

本文言語英語
ページ(範囲)2655-2691
ページ数37
ジャーナルAlgebraic and Geometric Topology
14
5
DOI
出版ステータス出版済み - 11 6 2014

All Science Journal Classification (ASJC) codes

  • 幾何学とトポロジー

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